Planar Projections of Graphs

Aravind, N. R. and Maniyar, Udit (2020) Planar Projections of Graphs. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 12016. pp. 453-462. ISSN 0302-9743

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Abstract

We introduce and study a new graph representation where vertices are embedded in three or more dimensions, and in which the edges are drawn on the projections onto the axis-parallel planes. We show that the complete graph on n vertices has a representation in \sqrt{n/2}+1 \rceil planes. In 3 dimensions, we show that there exist graphs with edges that can be projected onto two orthogonal planes, and that this is best possible. Finally, we obtain bounds in terms of parameters such as geometric thickness and linear arboricity. Using such a bound, we show that every graph of maximum degree 5 has a plane-projectable representation in 3 dimensions.

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IITH Creators:
IITH CreatorsORCiD
Aravind, N Rhttps://orcid.org/0000-0002-6590-7952
Maniyar, UditUNSPECIFIED
Item Type: Article
Uncontrolled Keywords: Complete graphs; Graph drawing; Graph representation; Orthogonal plane; Parallel planes; Planar projection; Planarity; Thickness
Subjects: Computer science
Divisions: Department of Computer Science & Engineering
Depositing User: . LibTrainee 2021
Date Deposited: 30 Jul 2021 04:21
Last Modified: 07 Mar 2022 06:14
URI: http://raiith.iith.ac.in/id/eprint/8570
Publisher URL: http://doi.org/10.1007/978-3-030-39219-2_36
OA policy: https://v2.sherpa.ac.uk/id/publication/36728
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